WASHINGTON — Three years after the opening of the Smithsonian’s landmark Museum of African American History and Culture, momentum is building toward the creation of a museum dedicated to American women’s history.

The House of Representatives on Tuesday passed a bill to establish the museum inside the Smithsonian network and take steps toward funding and construction. The vote was 374-37.

“Seeing role models doing things we all aspire to can change the course of someone’s life,” said Rep. Carolyn Maloney (D-NY), one of the bill’s principal sponsors. “Women and men of all ages deserve to see and be inspired by the remarkable women who helped shape this nation.”

“Our country should know the names of its history-making women,” said Rep. Eleanor Holmes Norton, the District of Columbia’s non-voting delegate. “Women have helped the United States since our founding, despite not being recognized for our many accomplishments.”

Linda St. Thomas, spokeswoman for the Smithsonian, said the existing museum network already makes a point of showcasing the historical contributions of American women through displays in venues like the African American museum, the Air and Space Museum and the Museum of American History. A new facility, she said, would naturally gather some of these existing artifacts and displays together while developing its own dedicated programming.

A similar bill is working its way through the Senate. But the path from congressional approval to opening day can be a long one. The bill to create the African American museum passed in 2003 but the museum itself didn’t open its doors until September 2016.

St. Thomas said once the Senate also gives its approval, which is expected later this year, the discussion will turn to funding. She said she expected the new museum to be 50/50 funding project between government money and private donations.

The nonpartisan Congressional Budget Office has put forth an official estimate that a proposed 350,000 square foot museum would cost $375 million to build. The 400,000 square foot African American History museum cost $540 million and was funded through a similar 50/50 public-private partnership.